Question

Under isothermal condition, energy $E$ is supplied to a soap bubble of surface tension $\sigma$ and radius $r$ to double the radius of the soap bubble. The value of $E$ is:

• A. $16\pi r^2\sigma$
• B. $24\pi r^2\sigma$
• C. $8\pi r^2\sigma$
• D. $12\pi r^2\sigma$

Answer 1

The correct option is B $24\pi r^2\sigma$

Surface tension of soap is $\sigma$

Given : $r_1=r$ $r_2=2r$

Soap bubble has two layers, thus it has two surfaces (inside and outside).

$\therefore$ Total surface area of smaller bubble $A_1=2\times 4\pi r_1^2=8\pi r^2$

Also total surface area of bigger bubble $A_2=2\times 4\pi r_2^2=2\times 4\pi (2r{)}^2=32\pi r^2$

Thus net change in surface area $\Delta A=A_2-A_1=32\pi r^2-8\pi r^2=24\pi r^2$

Energy supplied to increase the radius of bubble $E=\sigma \times \Delta A=24\pi r^2\sigma$